Thanks! Then perhaps Sage should raise an exception when it gets back genus -1 from singular.
Victor On Nov 22, 3:12 am, luisfe <[email protected]> wrote: > On Nov 21, 6:22 am, VictorMiller <[email protected]> wrote: > > > sage: T.<t1,t2,u1,u2> = QQ[] > > sage: TJ = Ideal([t1^2 + u1^2 - 1,t2^2 + u2^2 - 1, (t1-t2)^2 + (u1- > > u2)^2 -1]) > > sage: TJ.genus() > > 4294967295 > > sage: TJ.dimension() > > 1 > > Yes, there is a bug in the code. If I try Sage 32 bits, the answer to > TJ.genus() is -1. Is I use Sage 64 bits I get your result. > > The genus -1 looks like the ideal is not (absolutely) prime. This > looks odd at first sight since the ideal is prime over the rationals > and the projection onto [t1,t2] or [u1,u2] gives rational curves. > But, after a little research the answer looks right. > > sage: T.<t1,t2,u1,u2,t>=QQ[sqrt(3)][] > sage: TJ = Ideal([t1^2 + u1^2 - 1,t2^2 + u2^2 - 1, (t1-t2)^2 + (u1- > u2)^2 -1]) > sage: TJ.is_prime() > False > sage: TJ.primary_decomposition() > [Ideal (3*t2 + (-2*sqrt3)*u1 + (sqrt3)*u2, 3*t1 + (-sqrt3)*u1 + > (2*sqrt3)*u2, 4*u1^2 - 4*u1*u2 + 4*u2^2 - 3) of Multivariate > Polynomial Ring in t1, t2, u1, u2, t over Number Field in sqrt3 with > defining polynomial x^2 - 3, Ideal (3*t2 + (2*sqrt3)*u1 + (-sqrt3)*u2, > 3*t1 + (sqrt3)*u1 + (-2*sqrt3)*u2, 4*u1^2 - 4*u1*u2 + 4*u2^2 - 3) of > Multivariate Polynomial Ring in t1, t2, u1, u2, t over Number Field in > sqrt3 with defining polynomial x^2 - 3] > > The ideal is the union of two rational conjugate curves. -- To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
